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Living_dreams Group Title

find all local max,min and/or saddle point of f(x,y)=4+x^3+y^-3xy

  • 2 years ago
  • 2 years ago

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  1. Avva Group Title
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    would you plz write the function using equation

    • 2 years ago
  2. amistre64 Group Title
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    hmm, something to do with:\[f_{xy}f_{yx}-(f_{xx})^2\] or did i recall that incorrectly?

    • 2 years ago
  3. amistre64 Group Title
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    almost had it :) \[f_{xx}f_{yy}-(f_{xy})^2\]

    • 2 years ago
  4. Living_dreams Group Title
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    \[4+x ^{3}+y ^{3}-3xy\]

    • 2 years ago
  5. Living_dreams Group Title
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    it fxx.fyy-(fxy)^2

    • 2 years ago
  6. Living_dreams Group Title
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    i jst want to verify the answer for it !

    • 2 years ago
  7. TuringTest Group Title
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    what answer did you get?

    • 2 years ago
  8. Avva Group Title
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    \[fx = 2x-3y \] \[fy= 2y-3x\] on solving both equations the point is (0,0) \[fxx = 2\] , \[fyy= 2\] \[fxy = \] \[D = -5 <0 saddle point\]

    • 2 years ago
  9. TuringTest Group Title
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    that's not quite right I don't think

    • 2 years ago
  10. Avva Group Title
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    fxy = -3

    • 2 years ago
  11. TuringTest Group Title
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    \[f(x,y)=4+x^3+y^3-3xy\]\[f_x=3x^2-3y=0\implies y=x^2\]\[f_y=3y^2-3x=3x^4-3x=3x^3(x-1)=0\]\[ x=\{0,1\},y=\{0,1\}\]

    • 2 years ago
  12. Living_dreams Group Title
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    its x^3 so i have (0,0) ,(1,1)and a (-1,1) i am not sure if (-1,1) should be there oor not

    • 2 years ago
  13. Avva Group Title
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    @Living_dreams I solved what you mentioned in your comment

    • 2 years ago
  14. TuringTest Group Title
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    there is no x=-1 solution, I don't see how you get that

    • 2 years ago
  15. TuringTest Group Title
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    @Avva I don't see how you get your fx and fy

    • 2 years ago
  16. Avva Group Title
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    Ooh I saw the powers on X ^ y 2 not 3

    • 2 years ago
  17. Living_dreams Group Title
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    @Avva thanks for ur help but i was wonder abt the max and min points! n\ @TuringTest : 3y^2-3x=0 i sub y=x^2 from other equation so it will be 3x(x^3-1)=0 therefore you have x =0,1,-1 i am not sure abt -1 though !! tht was my question

    • 2 years ago
  18. TuringTest Group Title
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    x^3=1 does not have x=-1 as a solution since (-1)^3=-1, not 1

    • 2 years ago
  19. TuringTest Group Title
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    I did screw up my factoring earlier though, you were right about that :P

    • 2 years ago
  20. TuringTest Group Title
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    3x(x^3-1)=0 3x=0 -> x=0 x^3=1 -> x=1

    • 2 years ago
  21. Living_dreams Group Title
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    @TuringTest that alrite!! :) so now my question is x^3=1 so will i hv x=-1 if i solve for x ?

    • 2 years ago
  22. TuringTest Group Title
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    no, again, because \((-1)^3\neq1\) so \(x^3=1\) has only one real solution, x=1 x=-1 is NOT a solution

    • 2 years ago
  23. Avva Group Title
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    the other two roots are complex not real

    • 2 years ago
  24. Living_dreams Group Title
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    @TuringTest oh ok thanks a lot for ur help!! so the final ans will be (0,0 ) is a saddle point and (1,1) will be a local minimum !

    • 2 years ago
  25. TuringTest Group Title
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    exactly :)

    • 2 years ago
  26. Living_dreams Group Title
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    @Avva :thanks for ur help !! :)

    • 2 years ago
  27. Avva Group Title
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    @Living_dreams URW :) sorry I didn't get that the powers are 3 at first

    • 2 years ago
  28. Living_dreams Group Title
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    it okay !!i knw it get hard to tell the difference between 2 and 3 if we type it in equation form !!

    • 2 years ago
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